Can you cast an instant during the upkeep step before your opponent's triggered abilities resolve?

When the upkeep step begins, any triggered abilities that trigger at the start of upkeep are placed on the stack. After that, the active player receives priority (CR 502.2, CR 116.3). At this point, any player may cast instants or activate abilities before the triggers resolve.

Priority works like this: the active player gets priority first. If they pass, the non-active player gets priority. Only when all players pass priority in succession with the stack in the same state does the top object on the stack resolve (CR 116.4). So yes, you can cast an instant in response to your opponent's upkeep trigger before it resolves.

It's also worth noting that if no triggered abilities trigger at the start of upkeep, the active player simply receives priority at the beginning of the step and may still cast instants at that time (CR 502.2).

Concrete example: Your opponent controls Howling Mine, which triggers at the start of their upkeep to make them draw a card. Before that trigger resolves, you cast Stifle targeting the trigger. Because you received priority after the trigger was put on the stack, this is perfectly legal — Stifle resolves first and counters the draw trigger.

Key rules: CR 502.2 (upkeep step), CR 116.3 (active player gets priority after triggers are placed on stack), CR 116.4 (stack resolves only when all players pass in succession).